Goal

The goal of this paper is to describe the level of agreement and a harmonized scale of severity applicable to several commonly used delirium instruments: the CAM-S, DRS-R-98, MDAS. We do this in the context of a single clinical research study, where a team of trained lay interviewers administered each instrument along with supporting stimulus assessments in the same group of patients.

Note: In writing the paper, use the term “features” instead of “signs/symptoms”.

Summary of Results

IRT Models (dichotomous outcomes) estimated for all three instruments: CAM-S, DRS-R-98, MDAS

The instrument item responses were dichotomized into “none” vs “any” symptom.

The model fit to 8 core items per instrument is good. The core items include Sleep disturbance, Perceptual disturbance, Psychomotor agitation/retardation, Orientation, Attention, Memory impairment, and Disorganized Thinking.

Initially the fit to the expanded item sets was unacceptably bad. Then we recoded the sleep disturbance item, combining the “none” and “mild” categories. The model fit was then acceptable.

Item Parameters have been co-calibrated

The MDAS and CAM-S items have been equated to the DRS-R-98.

The items used to link the MDAS to the DRS-R-98 are: Disorientation, Perceptual disturbance, Sleep/wake cycle disturbance, Short term memory impairment, Delusions, and Disorganized Thinking.

The items used to link the CAM-S to the DRS-R-98 are: Disorientation, Perceptual disturbance, Sleep/wake cycle disturbance, Psychomotor agitation, Psychomotor retardation, Attention and Disorganized Thinking.

Created item response theory plots for the dichotomous outcome models

Created plots for: Test Information function, Item characteristic curves, Test characteristic curves, and density plots of estimated latent scores.

Estimated thresholds for polytomous outcomes for all three instruments: CAM-S, DRS-R-98, MDAS

Used the equated item parameters from the previous step to estimate the thresholds for the polytomous outcomes.

Note: Some thresholds are missing for some items since the highest categories weren’t observed.

Created model for the CAM-S short form

Took the four items from the CAM-S item parameters estimated for the polytomous outcomes.

Created item response theory plots for the polytomous outcome models

Created plots for: Test Information function, Item characteristic curves, Test characteristic curves, and density plots of estimated latent scores.

Created the proposed tables/figures for the manuscript

The tables are the typical Table 1 and a table of model fit statistics. The figures include a plot showing the item thresholds, a test information curve, a scatter plot of the factor scores for the four instruments, and a test characteristic curve that can create a crosswalk between instruments.

Created nomograms crosswalk tables and figures for the appendix

I prefer the tables over the figures because there are only four tables but twelve figures.

Examined the difference in information provided using polytomous versus dichotomous outcomes

We were interested in whether we could use the items as dichotomous outcomes in the new instrument since it would make training to use the instrument easier. However, the higher category outcomes provide a lot of information at higher “Delirium Intensity” levels. We felt this would be needed for a severity instrument.

Update 1-8-2018: Test reliability

Added measures of test reliability. In the descriptive statistics section of the report, added item correlations and Cronbach’s alpha. In the model fitting section of the report, added McDonald’s omega.

Update 1-24-2018: “Level of consciousness” recoding

The handling of the item CAM-S 4 “Altered level of consciousness” in the polytomous model was wrong. The initial recoding of the item was correct. The response categories “Stupor” and “Coma” were recoded as “Lethargic”, but since there weren’t any responses in those categories, there was nothing to recode. The responses for this item are nominal (“Normal”, “Vigilant”, “Lethargic”) so it’s wrong to treat it as ordered categories in the CFA model.

There are several options were considered to fix the coding. One is to collapse the response categories so that it becomes “Normal” vs “Abnormal / Everything else”. Another is, since there are few “Vigilant” responses, to recode these to missing or “Normal” and the item becomes “Normal” vs “Lethargic”. Another way is to turn the item into two indicators: “Normal” vs “Vigilant” and “Normal” vs “Lethargic”.

Turning the item into two indicators is the approach used in this report. This approach retains all the information provided in the item.

Update 1-29-2017: Figure aesthitics

  • Figure 1: Removed the item number from the left hand column. Added an solid line above the rugplot. Labeled the rugplot. Created a new version of the figure, removing the left hand column and putting it into a legend.

  • Figure 2: Added a rugplot to the Information and Reliability plots

  • Figure 3: Made the dots smaller and more transparent

  • Figure 4: Added a rugplot to the test characteristic curve plot

Report

Data Processing

Read Data

The data comes from /BASIL/POSTED/DATA/DERIVED/clean/current/. On 9-17-2017, the data was copied to the folder /BASIL/Projects/DeliriumHarmonization/POSTED/DATA/DERIVED/clean/current/ to make the results reproducible.

The file has 352 subjects and 1190 interviews.

This analysis will only use baseline hospital visits and daily hospital visits. Interviews that are not complete are dropped. Interviews that are missing the CAM-S vds, the DRS vds, or the MDAS vds are dropped. There are three subjects that de-enrolled from the study and are dropped from the analysis. [11-9-2017 decision: Do not exclude these three subjecs.] After applying these filters there are 352 subjects and 1178 interviews remaining in the datafile.

Data recode

The items that were coded as Don’t Know, Refused, Uncertain were set to missing, and the response options were reordered such that no symptoms were 0 and any symptoms were positive values.

The DRS, MDAS, CAM-S items are dichotomized to None vs Any symptom.

It is always possible once the item parameters are calibrated in the dichotomous setting to go back to the polytomous response setting. However, there should be at least 5% in the response categories and that is not always the case. So, we may end up in a situation where some items are dichotomous and others are polytomous. This makes the interpretation more difficult.

Item reference table

This table is a reference for the following tables to link item numbers to item content

DRS

Item Content
rdrs01 Sleep-wake cycle disturbance
rdrs02 Perceptual disturbances and hallucinations
rdrs03 Delusions
rdrs04 Lability of affect
rdrs05 Language
rdrs06 Thought process abnormalities
rdrs07 Motor agitation
rdrs08 Motor retardation
rdrs09 Orientation
rdrs10 Attention
rdrs11 Short-term memory
rdrs12 Long-term memory
rdrs13 Visuospatial ability

MDAS

Item Content
rmdas01 Reduced level of consciousness (Awareness)
rmdas02 Disorientation
rmdas03 Short-term memory impairment
rmdas04 Impaired digit span
rmdas05 Reduced ability to maintain and shift attention
rmdas06 Disorganized thinking
rmdas07 Perceptual disturbance
rmdas08 Delusions
rmdas09 Decreased or increased psychomotor activity
rmdas10 Sleep-wake cycle disturbance

CAM-S

Item Content
rcamlf1a Acute change
rcamlf2a Inattention
rcamlf3a Disorganized thinking
rcamlf4a Altered level of consciousness
rcamlf4l Altered level of consciousness (Lethargic)
rcamlf4v Altered level of consciousness (Vigilant)
rcamlf5a Disorientation
rcamlf6a Memory impairment
rcamlf7a Perceptual disturbances
rcamlf8a Psychomotor agitation
rcamlf8d Psychomotor retardation
rcamlf9a Sleep-wake cycle disturbance

Descriptive statistics

Summary tables/statistics for DRS (N=1178)

Original item category frequencies (%)

Item 0 1 2 3 Missing
rdrs04 97.62 1.70 0.59 0.00 0.08
rdrs08 97.62 1.78 0.59 0.00 0.00
rdrs07 97.03 2.29 0.51 0.00 0.17
rdrs03 94.99 2.55 0.68 1.02 0.76
rdrs05 86.93 11.46 1.10 0.34 0.17
rdrs13 86.76 9.76 1.87 0.08 1.53
rdrs06 86.16 8.57 4.67 0.42 0.17
rdrs02 84.13 4.58 3.90 6.62 0.76
rdrs09 75.13 14.43 9.51 0.42 0.51
rdrs11 52.29 25.30 7.56 14.18 0.68
rdrs12 45.50 23.60 11.46 17.74 1.70
rdrs10 43.12 43.04 12.99 0.76 0.08
rdrs01 25.64 67.66 6.03 0.34 0.34

Dichotomized item category frequencies (%)

Item 0 1 Missing
rdrs04 97.62 2.29 0.08
rdrs08 97.62 2.38 0.00
rdrs07 97.03 2.80 0.17
rdrs03 94.99 4.24 0.76
rdrs01 93.29 6.37 0.34
rdrs05 86.93 12.90 0.17
rdrs13 86.76 11.71 1.53
rdrs06 86.16 13.67 0.17
rdrs02 84.13 15.11 0.76
rdrs09 75.13 24.36 0.51
rdrs11 52.29 47.03 0.68
rdrs12 45.50 52.80 1.70
rdrs10 43.12 56.79 0.08

Item correlations

rdrs01 rdrs02 rdrs03 rdrs04 rdrs05 rdrs06 rdrs07 rdrs08 rdrs09 rdrs10 rdrs11 rdrs12 rdrs13
rdrs01 NA 0.11 0.05 0.15 0.18 0.17 0.08 0.16 0.12 0.09 0.11 0.10 0.06
rdrs02 0.11 NA 0.22 0.16 0.11 0.37 0.13 0.03 0.17 0.23 0.09 0.06 0.16
rdrs03 0.05 0.22 NA 0.24 0.12 0.36 0.13 0.03 0.11 0.13 0.07 0.09 0.10
rdrs04 0.15 0.16 0.24 NA 0.11 0.22 0.29 0.13 0.08 0.08 0.05 0.04 0.03
rdrs05 0.18 0.11 0.12 0.11 NA 0.34 0.23 0.09 0.23 0.22 0.25 0.25 0.24
rdrs06 0.17 0.37 0.36 0.22 0.34 NA 0.22 0.10 0.37 0.31 0.24 0.23 0.31
rdrs07 0.08 0.13 0.13 0.29 0.23 0.22 NA 0.04 0.13 0.12 0.11 0.10 0.19
rdrs08 0.16 0.03 0.03 0.13 0.09 0.10 0.04 NA 0.16 0.09 0.07 0.06 0.07
rdrs09 0.12 0.17 0.11 0.08 0.23 0.37 0.13 0.16 NA 0.33 0.31 0.32 0.16
rdrs10 0.09 0.23 0.13 0.08 0.22 0.31 0.12 0.09 0.33 NA 0.37 0.37 0.22
rdrs11 0.11 0.09 0.07 0.05 0.25 0.24 0.11 0.07 0.31 0.37 NA 0.84 0.28
rdrs12 0.10 0.06 0.09 0.04 0.25 0.23 0.10 0.06 0.32 0.37 0.84 NA 0.29
rdrs13 0.06 0.16 0.10 0.03 0.24 0.31 0.19 0.07 0.16 0.22 0.28 0.29 NA

Item - total score correlation

Correlation between the item and the sum of the dichotomous items.

total score
rdrs01 0.31
rdrs02 0.42
rdrs03 0.33
rdrs04 0.24
rdrs05 0.51
rdrs06 0.63
rdrs07 0.31
rdrs08 0.22
rdrs09 0.59
rdrs10 0.64
rdrs11 0.72
rdrs12 0.71
rdrs13 0.50

Cronbach’s alpha

## 
## Reliability analysis   
## Call: psych::alpha(x = .)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N    ase mean   sd
##       0.75      0.73    0.76      0.17 2.7 0.0097  0.2 0.17
## 
##  lower alpha upper     95% confidence boundaries
## 0.73 0.75 0.77 
## 
##  Reliability if an item is dropped:
##        raw_alpha std.alpha G6(smc) average_r S/N alpha se
## rdrs01      0.75      0.73    0.76      0.19 2.7   0.0098
## rdrs02      0.74      0.72    0.75      0.18 2.6   0.0097
## rdrs03      0.74      0.73    0.76      0.18 2.7   0.0099
## rdrs04      0.75      0.73    0.76      0.18 2.7   0.0098
## rdrs05      0.73      0.71    0.74      0.17 2.5   0.0103
## rdrs06      0.71      0.69    0.72      0.16 2.2   0.0108
## rdrs07      0.74      0.73    0.75      0.18 2.6   0.0099
## rdrs08      0.75      0.74    0.77      0.19 2.8   0.0098
## rdrs09      0.72      0.71    0.74      0.17 2.4   0.0106
## rdrs10      0.72      0.71    0.74      0.17 2.4   0.0109
## rdrs11      0.70      0.70    0.71      0.16 2.4   0.0117
## rdrs12      0.70      0.70    0.71      0.16 2.4   0.0116
## rdrs13      0.73      0.72    0.75      0.17 2.5   0.0103
## 
##  Item statistics 
##           n raw.r std.r r.cor r.drop  mean   sd
## rdrs01 1174  0.32  0.38  0.27   0.21 0.064 0.24
## rdrs02 1169  0.43  0.44  0.35   0.28 0.152 0.36
## rdrs03 1169  0.33  0.41  0.32   0.24 0.043 0.20
## rdrs04 1177  0.29  0.40  0.30   0.20 0.023 0.15
## rdrs05 1176  0.52  0.53  0.46   0.39 0.129 0.34
## rdrs06 1176  0.64  0.66  0.65   0.53 0.137 0.34
## rdrs07 1176  0.34  0.43  0.34   0.25 0.028 0.17
## rdrs08 1178  0.23  0.32  0.20   0.16 0.024 0.15
## rdrs09 1172  0.59  0.55  0.49   0.44 0.245 0.43
## rdrs10 1177  0.63  0.56  0.51   0.48 0.568 0.50
## rdrs11 1170  0.72  0.60  0.63   0.57 0.474 0.50
## rdrs12 1158  0.71  0.59  0.62   0.56 0.537 0.50
## rdrs13 1160  0.50  0.48  0.41   0.37 0.119 0.32
## 
## Non missing response frequency for each item
##           0    1 miss
## rdrs01 0.94 0.06 0.00
## rdrs02 0.85 0.15 0.01
## rdrs03 0.96 0.04 0.01
## rdrs04 0.98 0.02 0.00
## rdrs05 0.87 0.13 0.00
## rdrs06 0.86 0.14 0.00
## rdrs07 0.97 0.03 0.00
## rdrs08 0.98 0.02 0.00
## rdrs09 0.76 0.24 0.01
## rdrs10 0.43 0.57 0.00
## rdrs11 0.53 0.47 0.01
## rdrs12 0.46 0.54 0.02
## rdrs13 0.88 0.12 0.02

Summary tables/statistics for MDAS (N=1178)

Original item category frequencies (%)

Item 0 1 2 3 Missing
rmdas08 94.91 3.23 1.10 0.08 0.68
rmdas09 94.91 3.74 1.27 0.00 0.08
rmdas01 94.57 4.16 1.19 0.00 0.08
rmdas06 84.55 10.70 4.16 0.59 0.00
rmdas07 84.21 12.82 2.21 0.08 0.68
rmdas02 76.40 14.18 5.69 3.14 0.59
rmdas05 58.74 29.20 11.12 0.93 0.00
rmdas03 51.19 23.68 18.76 5.69 0.68
rmdas04 29.20 57.22 12.56 0.59 0.42
rmdas10 25.47 68.85 5.01 0.34 0.34

Dichotomized item category frequencies (%)

Item 0 1 Missing
rmdas08 94.91 4.41 0.68
rmdas09 94.91 5.01 0.08
rmdas01 94.57 5.35 0.08
rmdas10 94.31 5.35 0.34
rmdas06 84.55 15.45 0.00
rmdas07 84.21 15.11 0.68
rmdas02 76.40 23.01 0.59
rmdas05 58.74 41.26 0.00
rmdas03 51.19 48.13 0.68
rmdas04 29.20 70.37 0.42

Item correlations

rmdas01 rmdas02 rmdas03 rmdas04 rmdas05 rmdas06 rmdas07 rmdas08 rmdas09 rmdas10
rmdas01 NA 0.26 0.15 0.10 0.25 0.36 0.20 0.12 0.33 0.22
rmdas02 0.26 NA 0.38 0.19 0.37 0.44 0.18 0.12 0.19 0.11
rmdas03 0.15 0.38 NA 0.27 0.34 0.27 0.10 0.08 0.12 0.09
rmdas04 0.10 0.19 0.27 NA 0.32 0.16 0.13 0.09 0.05 0.06
rmdas05 0.25 0.37 0.34 0.32 NA 0.42 0.26 0.16 0.17 0.08
rmdas06 0.36 0.44 0.27 0.16 0.42 NA 0.37 0.36 0.27 0.14
rmdas07 0.20 0.18 0.10 0.13 0.26 0.37 NA 0.24 0.08 0.08
rmdas08 0.12 0.12 0.08 0.09 0.16 0.36 0.24 NA 0.09 0.08
rmdas09 0.33 0.19 0.12 0.05 0.17 0.27 0.08 0.09 NA 0.14
rmdas10 0.22 0.11 0.09 0.06 0.08 0.14 0.08 0.08 0.14 NA

Item - total score correlation

Correlation between the item and the sum of the dichotomous items.

total score
rmdas01 0.47
rmdas02 0.65
rmdas03 0.62
rmdas04 0.52
rmdas05 0.71
rmdas06 0.69
rmdas07 0.49
rmdas08 0.36
rmdas09 0.36
rmdas10 0.29

Cronbach’s alpha

## 
## Reliability analysis   
## Call: psych::alpha(x = .)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N   ase mean   sd
##       0.71      0.71    0.72       0.2 2.5 0.012 0.24 0.19
## 
##  lower alpha upper     95% confidence boundaries
## 0.69 0.71 0.73 
## 
##  Reliability if an item is dropped:
##         raw_alpha std.alpha G6(smc) average_r S/N alpha se
## rmdas01      0.69      0.68    0.68      0.19 2.2    0.012
## rmdas02      0.66      0.67    0.67      0.19 2.1    0.014
## rmdas03      0.68      0.69    0.69      0.20 2.2    0.013
## rmdas04      0.70      0.70    0.71      0.21 2.4    0.012
## rmdas05      0.65      0.67    0.67      0.18 2.0    0.014
## rmdas06      0.65      0.65    0.65      0.17 1.9    0.014
## rmdas07      0.69      0.70    0.70      0.20 2.3    0.012
## rmdas08      0.70      0.71    0.71      0.21 2.4    0.012
## rmdas09      0.70      0.70    0.70      0.21 2.4    0.012
## rmdas10      0.71      0.72    0.72      0.22 2.5    0.012
## 
##  Item statistics 
##            n raw.r std.r r.cor r.drop  mean   sd
## rmdas01 1177  0.49  0.56  0.49   0.38 0.054 0.23
## rmdas02 1171  0.65  0.61  0.56   0.50 0.231 0.42
## rmdas03 1170  0.62  0.53  0.45   0.41 0.485 0.50
## rmdas04 1173  0.52  0.45  0.34   0.31 0.707 0.46
## rmdas05 1178  0.70  0.64  0.60   0.54 0.413 0.49
## rmdas06 1178  0.70  0.71  0.71   0.57 0.154 0.36
## rmdas07 1170  0.49  0.50  0.40   0.32 0.152 0.36
## rmdas08 1170  0.36  0.44  0.33   0.26 0.044 0.21
## rmdas09 1177  0.38  0.46  0.35   0.27 0.050 0.22
## rmdas10 1174  0.29  0.38  0.24   0.18 0.054 0.23
## 
## Non missing response frequency for each item
##            0    1 miss
## rmdas01 0.95 0.05 0.00
## rmdas02 0.77 0.23 0.01
## rmdas03 0.52 0.48 0.01
## rmdas04 0.29 0.71 0.00
## rmdas05 0.59 0.41 0.00
## rmdas06 0.85 0.15 0.00
## rmdas07 0.85 0.15 0.01
## rmdas08 0.96 0.04 0.01
## rmdas09 0.95 0.05 0.00
## rmdas10 0.95 0.05 0.00

Summary tables/statistics for CAM-S (N=1178)

Original item category frequencies (%)

Item 0 1 2 Missing
rcamlf4v 99.83 0.17 0.00 0.00
rcamlf8d 97.45 2.29 0.25 0.00
rcamlf8a 97.28 2.38 0.34 0.00
rcamlf4l 96.60 3.40 0.00 0.00
rcamlf7a 85.82 12.14 1.36 0.68
rcamlf3a 84.47 12.14 3.40 0.00
rcamlf5a 76.40 15.87 7.13 0.59
rcamlf1a 74.19 25.04 0.00 0.76
rcamlf6a 72.58 22.75 3.99 0.68
rcamlf2a 42.02 44.23 13.58 0.17
rcamlf9a 25.04 68.85 5.69 0.42

Dichotomized item category frequency (%)

Item 0 1 Missing
rcamlf4v 99.83 0.17 0.00
rcamlf8d 97.45 2.55 0.00
rcamlf8a 97.28 2.72 0.00
rcamlf4l 96.60 3.40 0.00
rcamlf9a 93.89 5.69 0.42
rcamlf7a 85.82 13.50 0.68
rcamlf3a 84.47 15.53 0.00
rcamlf5a 76.40 23.01 0.59
rcamlf1a 74.19 25.04 0.76
rcamlf6a 72.58 26.74 0.68
rcamlf2a 42.02 57.81 0.17

Item correlations

rcamlf1a rcamlf2a rcamlf3a rcamlf4l rcamlf4v rcamlf5a rcamlf6a rcamlf7a rcamlf8a rcamlf8d rcamlf9a
rcamlf1a NA 0.33 0.52 0.25 0.07 0.35 0.27 0.67 0.17 0.09 0.13
rcamlf2a 0.33 NA 0.33 0.15 0.04 0.35 0.37 0.22 0.11 0.08 0.06
rcamlf3a 0.52 0.33 NA 0.22 0.04 0.44 0.38 0.38 0.25 0.12 0.16
rcamlf4l 0.25 0.15 0.22 NA -0.01 0.16 0.17 0.17 0.08 0.18 0.31
rcamlf4v 0.07 0.04 0.04 -0.01 NA 0.03 0.07 0.10 0.25 -0.01 -0.01
rcamlf5a 0.35 0.35 0.44 0.16 0.03 NA 0.43 0.23 0.13 0.14 0.09
rcamlf6a 0.27 0.37 0.38 0.17 0.07 0.43 NA 0.18 0.16 0.08 0.10
rcamlf7a 0.67 0.22 0.38 0.17 0.10 0.23 0.18 NA 0.10 0.00 0.09
rcamlf8a 0.17 0.11 0.25 0.08 0.25 0.13 0.16 0.10 NA 0.04 0.03
rcamlf8d 0.09 0.08 0.12 0.18 -0.01 0.14 0.08 0.00 0.04 NA 0.10
rcamlf9a 0.13 0.06 0.16 0.31 -0.01 0.09 0.10 0.09 0.03 0.10 NA

Item - total score correlation

Correlation between the item and the sum of the dichotomous items.

total score
rcamlf1a 0.74
rcamlf2a 0.64
rcamlf3a 0.72
rcamlf4l 0.39
rcamlf4v 0.11
rcamlf5a 0.67
rcamlf6a 0.65
rcamlf7a 0.60
rcamlf8a 0.30
rcamlf8d 0.23
rcamlf9a 0.30

Cronbach’s alpha

## 
## Reliability analysis   
## Call: psych::alpha(x = .)
## 
##   raw_alpha std.alpha G6(smc) average_r S/N    ase mean   sd
##       0.73      0.71    0.73      0.18 2.4 0.0098 0.16 0.17
## 
##  lower alpha upper     95% confidence boundaries
## 0.72 0.73 0.75 
## 
##  Reliability if an item is dropped:
##          raw_alpha std.alpha G6(smc) average_r S/N alpha se
## rcamlf1a      0.68      0.65    0.66      0.16 1.8   0.0120
## rcamlf2a      0.71      0.68    0.71      0.17 2.1   0.0106
## rcamlf3a      0.68      0.65    0.68      0.16 1.9   0.0118
## rcamlf4l      0.73      0.69    0.72      0.18 2.2   0.0101
## rcamlf4v      0.74      0.72    0.74      0.21 2.6   0.0099
## rcamlf5a      0.69      0.67    0.69      0.17 2.0   0.0113
## rcamlf6a      0.70      0.67    0.70      0.17 2.1   0.0108
## rcamlf7a      0.70      0.67    0.69      0.17 2.1   0.0107
## rcamlf8a      0.73      0.70    0.72      0.19 2.4   0.0100
## rcamlf8d      0.74      0.72    0.74      0.20 2.5   0.0098
## rcamlf9a      0.74      0.71    0.73      0.20 2.4   0.0097
## 
##  Item statistics 
##             n raw.r std.r r.cor r.drop   mean    sd
## rcamlf1a 1169  0.74  0.69  0.72  0.604 0.2524 0.435
## rcamlf2a 1176  0.64  0.55  0.48  0.445 0.5791 0.494
## rcamlf3a 1178  0.72  0.69  0.68  0.606 0.1553 0.362
## rcamlf4l 1178  0.40  0.48  0.38  0.309 0.0340 0.181
## rcamlf4v 1178  0.11  0.28  0.14  0.093 0.0017 0.041
## rcamlf5a 1171  0.67  0.60  0.56  0.512 0.2314 0.422
## rcamlf6a 1170  0.64  0.57  0.52  0.466 0.2692 0.444
## rcamlf7a 1170  0.60  0.56  0.55  0.456 0.1359 0.343
## rcamlf8a 1178  0.31  0.41  0.30  0.219 0.0272 0.163
## rcamlf8d 1178  0.24  0.33  0.19  0.150 0.0255 0.158
## rcamlf9a 1173  0.30  0.37  0.24  0.180 0.0571 0.232
## 
## Non missing response frequency for each item
##             0    1 miss
## rcamlf1a 0.75 0.25 0.01
## rcamlf2a 0.42 0.58 0.00
## rcamlf3a 0.84 0.16 0.00
## rcamlf4l 0.97 0.03 0.00
## rcamlf4v 1.00 0.00 0.00
## rcamlf5a 0.77 0.23 0.01
## rcamlf6a 0.73 0.27 0.01
## rcamlf7a 0.86 0.14 0.01
## rcamlf8a 0.97 0.03 0.00
## rcamlf8d 0.97 0.03 0.00
## rcamlf9a 0.94 0.06 0.00
## 
## Running model: cfa-drs-1-1-2pl.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-drs-1-1-2pl.inp" 
## Reading model:  cfa-drs-1-1-2pl.out 
## 
## Running model: cfa-drs-2-1-2pl.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-drs-2-1-2pl.inp" 
## Reading model:  cfa-drs-2-1-2pl.out
## 
## Running model: cfa-drs-1-1-wlsmv.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-drs-1-1-wlsmv.inp" 
## Reading model:  cfa-drs-1-1-wlsmv.out 
## 
## Running model: cfa-drs-2-1-wlsmv.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-drs-2-1-wlsmv.inp" 
## Reading model:  cfa-drs-2-1-wlsmv.out
## 
## Running model: cfa-mdas-1-1-2pl.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-mdas-1-1-2pl.inp" 
## Reading model:  cfa-mdas-1-1-2pl.out 
## 
## Running model: cfa-mdas-2-1-2pl.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-mdas-2-1-2pl.inp" 
## Reading model:  cfa-mdas-2-1-2pl.out
## 
## Running model: cfa-mdas-1-1-wlsmv.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-mdas-1-1-wlsmv.inp" 
## Reading model:  cfa-mdas-1-1-wlsmv.out 
## 
## Running model: cfa-mdas-2-1-wlsmv.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-mdas-2-1-wlsmv.inp" 
## Reading model:  cfa-mdas-2-1-wlsmv.out
## 
## Running model: cfa-cam-1-1-2pl.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-cam-1-1-2pl.inp" 
## Reading model:  cfa-cam-1-1-2pl.out 
## 
## Running model: cfa-cam-2-1-2pl.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-cam-2-1-2pl.inp" 
## Reading model:  cfa-cam-2-1-2pl.out
## 
## Running model: cfa-cam-1-1-wlsmv.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-cam-1-1-wlsmv.inp" 
## Reading model:  cfa-cam-1-1-wlsmv.out 
## 
## Running model: cfa-cam-2-1-wlsmv.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-cam-2-1-wlsmv.inp" 
## Reading model:  cfa-cam-2-1-wlsmv.out

Model Fitting (Dichotomous model)

Fit CFA models

We will fit a CFA in the MDAS, DRS, and CAM-S individually then equate them. To ensure that the CFA covers the same dimension for each test, we are fitting the CFA to a core set of items in common across test and then add in the remaining items keeping the core item parameters fixed.

The core set of items are:

Feature DRS MDAS CAM-S
Sleep disturbance drs01 mdas10 camlf9a
Perceptual disturbance drs02 mdas07 camlf7a
Psychomotor agitation/retardation drs07, drs08 mdas09 camlf8a, camlf8d
Orientation drs09 mdas02 camlf5a
Attention drs10 mdas04, mdas05 camlf2a
Memory impairment drs11, drs12 mdas03 camlf6a
Disorganized thinking/thought process abnormalities drs06 mdas06 camlf3a

NOTE: In the original 2PL models, the sleep item did not fit well. To try to improve the fit, we tried changing to a 3PL model. This did not improve the fit. So, next we changed the way we dichotomized sleep. Instead of grouping the categories 0 vs 1, 2, 3, we used 0, 1 vs 2, 3. This helped improve the fit in the DRS and MDAS a lot and in the CAM-S a little.

DRS Confirmatory Factor Analysis

Fit statistics

Model 1
N CFI RMSEA
1178 0.98 0.03
Model 2
N CFI RMSEA
1178 0.97 0.08

Item Parameters

Model 1
Item Slope Threshold
rdrs06 3.54 4.31
rdrs10 2.66 -0.55
rdrs09 1.75 1.68
rdrs07 1.63 4.69
rdrs11 1.36 0.13
rdrs02 1.20 2.14
rdrs08 1.09 4.26
rdrs01 0.93 3.04
Model 2
Item Slope Threshold
rdrs06 3.54 4.31
rdrs10 2.66 -0.55
rdrs12 2.44 -0.31
rdrs09 1.75 1.68
rdrs07 1.63 4.69
rdrs13 1.61 2.75
rdrs05 1.59 2.67
rdrs03 1.51 4.02
rdrs04 1.49 4.75
rdrs11 1.36 0.13
rdrs02 1.20 2.14
rdrs08 1.09 4.26
rdrs01 0.93 3.04

The McDonald’s omega statistic for the DRS is 0.91.

MDAS Confirmatory Factor Analysis

Fit statistics

Model 1
N CFI RMSEA
1178 0.97 0.04
Model 2
N CFI RMSEA
1178 0.98 0.02

Item Parameters

Model 1
Item Slope Threshold
rmdas06 3.77 4.23
rmdas05 2.55 0.69
rmdas02 2.12 1.99
rmdas03 1.45 0.08
rmdas09 1.42 3.76
rmdas07 1.20 2.14
rmdas04 1.20 -1.12
rmdas10 0.80 3.14
Model 2
Item Slope Threshold
rmdas06 3.77 4.23
rmdas05 2.55 0.69
rmdas01 2.51 4.97
rmdas02 2.12 1.99
rmdas08 1.59 4.06
rmdas03 1.45 0.08
rmdas09 1.42 3.76
rmdas07 1.20 2.14
rmdas04 1.20 -1.12
rmdas10 0.80 3.14

The McDonald’s omega statistic for the MDAS is 0.89.

CAM-S Confirmatory Factor Analysis

Fit statistics

Model 1
N CFI RMSEA
1178 0.99 0.02
Model 2
N CFI RMSEA
1178 0.9 0.1

Item Parameters

Model 1
Item Slope Threshold
rcamlf3a 3.92 4.37
rcamlf2a 2.45 -0.60
rcamlf5a 2.27 2.09
rcamlf6a 1.96 1.59
rcamlf8a 1.65 4.74
rcamlf7a 1.36 2.40
rcamlf8d 1.01 4.11
rcamlf9a 0.73 3.03
Model 2
Item Slope Threshold
rcamlf3a 3.92 4.37
rcamlf1a 2.61 2.08
rcamlf2a 2.45 -0.60
rcamlf5a 2.27 2.09
rcamlf4v 2.07 8.41
rcamlf6a 1.96 1.59
rcamlf4l 1.87 4.75
rcamlf8a 1.65 4.74
rcamlf7a 1.36 2.40
rcamlf8d 1.01 4.11
rcamlf9a 0.73 3.03

The McDonald’s omega statistic for the CAM-S is 0.91.

Item equating

Using the SNSequate package to equate item parameters.

DRS item parameters

Item parameters for DRS with dichotomous outcomes
Item A B1
rdrs01 0.93 3.26
rdrs02 1.20 1.78
rdrs03 1.51 2.66
rdrs04 1.49 3.20
rdrs05 1.59 1.68
rdrs06 3.54 1.22
rdrs07 1.63 2.88
rdrs08 1.09 3.91
rdrs09 1.75 0.96
rdrs10 2.66 -0.21
rdrs11 1.36 0.10
rdrs12 2.44 -0.13
rdrs13 1.61 1.71

MDAS item parameters

Item parameters for MDAS with dichotomous outcomes
Item A B1
rmdas01 2.51 1.98
rmdas02 2.12 0.94
rmdas03 1.45 0.05
rmdas04 1.20 -0.94
rmdas05 2.55 0.27
rmdas06 3.77 1.12
rmdas07 1.20 1.78
rmdas08 1.59 2.55
rmdas09 1.42 2.64
rmdas10 0.80 3.95

CAM-S item parameters

Item parameters for CAM with dichotomous outcomes
Item A B1
rcamlf1a 2.61 0.80
rcamlf2a 2.45 -0.24
rcamlf3a 3.92 1.11
rcamlf4l 1.87 2.54
rcamlf4v 2.07 4.07
rcamlf5a 2.27 0.92
rcamlf6a 1.96 0.81
rcamlf7a 1.36 1.76
rcamlf8a 1.65 2.87
rcamlf8d 1.01 4.07
rcamlf9a 0.73 4.17

The items used to link the MDAS to the DRS are: Disorientation, Perceptual disturbance, Sleep/wake cycle disturbance, Short term memory impairment, Delusions, and Thought process abnormality/Disorganized thinking.

The items used to link the CAM-S to the DRS are: Disorientation, Perceptual disturbance, Sleep/wake cycle disturbance, Psychomotor agitation, Psychomotor retardation, Attention, and Thought process abnormality/Disorganized thinking.

## 
## Running model: cfa-mdas-link-1.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-mdas-link-1.inp" 
## Reading model:  cfa-mdas-link-1.out

MDAS item parameters linked

Comparision between original and linked item parameters for mdas
Item A (original) B (original) A (linked) B (linked)
rmdas01 2.51 1.98 2.33 2.00
rmdas02 2.12 0.94 1.97 0.88
rmdas03 1.45 0.05 1.34 -0.07
rmdas04 1.20 -0.94 1.11 -1.14
rmdas05 2.55 0.27 2.37 0.16
rmdas06 3.77 1.12 3.50 1.08
rmdas07 1.20 1.78 1.12 1.79
rmdas08 1.59 2.55 1.48 2.62
rmdas09 1.42 2.64 1.32 2.71
rmdas10 0.80 3.95 0.74 4.12
## 
## Running model: cfa-cam-link-1.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-cam-link-1.inp" 
## Reading model:  cfa-cam-link-1.out

CAM-S item parameters linked

Comparision between original and linked item parameters for cam
Item A (original) B (original) A (linked) B (linked)
rcamlf1a 2.61 0.80 2.54 0.86
rcamlf2a 2.45 -0.24 2.39 -0.21
rcamlf3a 3.92 1.11 3.82 1.18
rcamlf4l 1.87 2.54 1.82 2.64
rcamlf4v 2.07 4.07 2.02 4.20
rcamlf5a 2.27 0.92 2.22 0.98
rcamlf6a 1.96 0.81 1.91 0.87
rcamlf7a 1.36 1.76 1.33 1.85
rcamlf8a 1.65 2.87 1.61 2.98
rcamlf8d 1.01 4.07 0.98 4.21
rcamlf9a 0.73 4.17 0.71 4.31

Plots for the dichotomous model

## Reading model:  cfa-drs-2-1-2pl.out
## Reading model:  cfa-mdas-link-1.out
## Reading model:  cfa-cam-link-1.out

Model Fitting (Polytomous model)

DRS CFA model with polytomous outcome

## 
## Running model: cfa-drs-3-1.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-drs-3-1.inp" 
## Reading model:  cfa-drs-3-1.out
Item parameters for DRS with polytomous outcomes
Item A B1 B2 B3
rdrs01 0.93 -1.31 3.26 6.57
rdrs02 1.20 1.78 2.17 2.64
rdrs03 1.51 2.66 3.33 3.68
rdrs04 1.49 3.20 4.19 NA
rdrs05 1.59 1.68 3.40 4.44
rdrs06 3.54 1.22 1.80 2.94
rdrs07 1.63 2.88 4.06 NA
rdrs08 1.09 3.91 5.23 NA
rdrs09 1.75 0.96 1.80 3.98
rdrs10 2.66 -0.21 1.29 3.02
rdrs11 1.36 0.10 1.26 1.77
rdrs12 2.44 -0.13 0.63 1.08
rdrs13 1.61 1.71 3.10 5.16

MDAS CFA model with polytomous outcome

## 
## Running model: cfa-mdas-3-1.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-mdas-3-1.inp" 
## Reading model:  cfa-mdas-3-1.out
Item parameters for MDAS with polytomous outcomes
Item A B1 B2 B3
rmdas01 2.33 2.00 2.97 NA
rmdas02 1.97 0.88 1.75 2.53
rmdas03 1.34 -0.07 1.02 2.59
rmdas04 1.11 -1.14 1.97 5.14
rmdas05 2.37 0.16 1.41 3.14
rmdas06 3.50 1.08 1.89 3.07
rmdas07 1.12 1.79 3.82 6.85
rmdas08 1.48 2.62 3.61 5.44
rmdas09 1.32 2.71 3.93 NA
rmdas10 0.74 -1.71 4.12 7.99

CAM-S CFA model with polytomous outcome

## 
## Running model: cfa-cam-3-1.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-cam-3-1.inp" 
## Reading model:  cfa-cam-3-1.out
Item parameters for CAM with polytomous outcomes
Item A B1 B2
rcamlf1a 2.54 0.86 NA
rcamlf2a 2.39 -0.21 1.41
rcamlf3a 3.82 1.18 2.06
rcamlf4l 1.82 2.64 NA
rcamlf4v 2.02 4.20 NA
rcamlf5a 2.22 0.98 1.89
rcamlf6a 1.91 0.87 2.43
rcamlf7a 1.33 1.85 3.88
rcamlf8a 1.61 2.98 4.36
rcamlf8d 0.98 4.21 6.61
rcamlf9a 0.71 -1.67 4.31
## 
## Running model: cfa-camsf-3-1.inp 
## System command: cd "." && "/Applications/Mplus/mplus" "cfa-camsf-3-1.inp" 
## Reading model:  cfa-camsf-3-1.out

Plots for the polytomous model

For the manuscript

This section contains tables/figures for the manuscript.

Table 1

Variable N Mean SD Count Percent
adlany 342 NA NA 272 79.5
age 352 80.3 6.8 NA NA
dementia 352 NA NA 101 28.7
educ 344 14.5 3.0 NA NA
female 352 NA NA 207 58.8
livesalone 348 NA NA 133 38.2
married 348 NA NA 139 39.9
nonwhite 352 NA NA 51 14.5
surgical 352 NA NA 102 29.0

Table 2

Summary of delirium severity instruments from all hospital interviews.
Variable N Mean SD Min Median Max
CAMS.LF 1178 2.3 2.4 0 1 14
CAMS.SF 1178 0.7 1.3 0 0 6
DRS 1178 4.7 4.3 0 3 28
MDAS 1178 3.9 3.3 0 3 22

Table 3

Delirium Instrument CFI RMSEA
DRS (Model using only common features) 0.98 0.03
DRS (Model using all features) 0.97 0.08
MDAS (Model using only common features) 0.97 0.04
MDAS (Model using all features) 0.98 0.02
CAM-S (Model using only common features) 0.99 0.02
CAM-S (Model using all features) 0.90 0.10
* CFI = Confirmatory Fit Index, RMSEA = Root Mean Squared Error of Approximation
Values indicating good fit are: CFI>.9, RMSEA<.06

Figure 1

Figure 2

Figure 3

Figure 4

For the appendix

This section contains tables/figures for the appendix.

Tables of item parameters

Parameters are unstandardized factor loading and thresholds from the final mplus output. Considered adding standard errors to the table, but because in this final model we are estimating the thresholds for the more severe categories, all the other parameters have been constrained to previous estimates, so it would be difficult and may not make sense to include standard errors.

CAM-S long form

Item Factor loading Threshold 1 Threshold 2
camlf1a 2.545 2.179 NA
camlf2a 2.393 -0.507 3.364
camlf3a 3.823 4.510 7.884
camlf4l 1.822 4.814 NA
camlf4v 2.018 8.485 NA
camlf5a 2.218 2.171 4.201
camlf6a 1.908 1.661 4.627
camlf7a 1.326 2.447 5.151
camlf8a 1.608 4.796 7.016
camlf8d 0.985 4.147 6.506
camlf9a 0.708 -1.181 3.053

DRS-R-98

Item Factor loading Threshold 1 Threshold 2 Threshold 3
drs01 0.934 -1.228 3.044 6.133
drs02 1.204 2.141 2.614 3.184
drs03 1.514 4.024 5.037 5.579
drs04 1.485 4.750 6.217 NA
drs05 1.589 2.667 5.400 7.052
drs06 3.542 4.310 6.391 10.428
drs07 1.629 4.687 6.607 NA
drs08 1.090 4.262 5.698 NA
drs09 1.748 1.675 3.139 6.962
drs10 2.665 -0.550 3.431 8.041
drs11 1.358 0.132 1.716 2.401
drs12 2.445 -0.311 1.545 2.652
drs13 1.607 2.754 4.974 8.292

MDAS

Item Factor loading Threshold 1 Threshold 2 Threshold 3
mdas01 2.332 4.667 6.921 NA
mdas02 1.965 1.733 3.434 4.964
mdas03 1.343 -0.097 1.371 3.482
mdas04 1.110 -1.269 2.192 5.707
mdas05 2.370 0.382 3.351 7.443
mdas06 3.504 3.776 6.634 10.757
mdas07 1.116 1.997 4.261 7.645
mdas08 1.477 3.869 5.339 8.042
mdas09 1.322 3.588 5.193 NA
mdas10 0.738 -1.265 3.042 5.899

Table A1: Nomogram Crosswalk tables

Table A1a: CAM-S LF table

CAM-S LF to MDAS, DRS-R-98, CAM-S SF
CAM-S LF MDAS DRS-R-98 CAM-S SF
0 0.2 0.1 0.0
1 1.9 1.5 0.2
2 3.3 3.7 0.8
3 4.6 5.5 1.3
4 5.8 7.2 1.8
5 6.9 8.7 2.3
6 8.0 10.2 2.9
7 9.2 11.8 3.4
8 10.4 13.4 3.9
9 11.8 15.1 4.4
10 13.1 16.7 4.8
11 14.7 18.5 5.2
12 16.4 20.7 5.5
13 18.4 23.3 5.8
14 20.4 26.0 6.1
15 21.8 28.4 6.3
16 23.0 30.6 6.6
17 24.2 32.7 6.9
18 25.8 34.7 7.0
19 27.1 35.7 7.0

Table A1b: MDAS table

MDAS to CAM-S LF, DRS-R-98 and CAM-S SF
MDAS CAM-S LF DRS-R-98 CAM-S SF
0 0.2 0.1 0.0
1 0.5 0.6 0.0
2 1.0 1.6 0.2
3 1.7 3.1 0.6
4 2.5 4.6 1.0
5 3.3 6.1 1.5
6 4.2 7.5 1.9
7 5.1 8.9 2.4
8 6.0 10.2 2.9
9 6.9 11.6 3.3
10 7.6 12.9 3.7
11 8.4 14.1 4.1
12 9.2 15.3 4.4
13 9.9 16.5 4.8
14 10.6 17.7 5.1
15 11.2 18.9 5.3
16 11.8 20.1 5.5
17 12.3 21.5 5.6
18 12.8 22.7 5.8
19 13.3 24.0 5.9
20 13.8 25.5 6.0
21 14.4 27.1 6.2
22 15.1 28.7 6.4
23 16.0 30.6 6.6
24 16.8 32.4 6.8
25 17.5 33.8 6.9
26 18.1 34.9 7.0
27 18.6 35.6 7.0

Table A1c: DRS-R-98 table

DRS-R-98 to CAM-S LF, MDAS and CAM-S SF
DRS-R-98 CAM-S LF MDAS CAM-S SF
0 0.2 0.2 0.0
1 0.7 1.5 0.1
2 1.2 2.3 0.3
3 1.7 2.9 0.6
4 2.2 3.6 0.9
5 2.7 4.2 1.1
6 3.3 4.9 1.4
7 3.9 5.7 1.8
8 4.5 6.4 2.1
9 5.2 7.1 2.4
10 5.9 7.8 2.8
11 6.5 8.5 3.1
12 7.1 9.3 3.5
13 7.7 10.1 3.8
14 8.3 10.9 4.0
15 9.0 11.7 4.3
16 9.6 12.6 4.6
17 10.2 13.4 4.9
18 10.8 14.3 5.1
19 11.3 15.1 5.3
20 11.7 15.9 5.5
21 12.1 16.6 5.6
22 12.5 17.5 5.7
23 12.9 18.2 5.8
24 13.2 18.9 5.9
25 13.6 19.7 6.0
26 14.0 20.4 6.1
27 14.4 21.0 6.2
28 14.8 21.6 6.3
29 15.2 22.1 6.4
30 15.7 22.7 6.5
31 16.2 23.2 6.7
32 16.7 23.8 6.8
33 17.1 24.4 6.9
34 17.6 25.1 7.0
35 18.2 26.1 7.0
36 18.7 27.1 7.0

Table A1d: CAM-S SF table

CAM-S SF to MDAS, DRS-R-98, CAM-S LF
CAM-S SF MDAS DRS-R-98 CAM-S LF
0 0.2 0.1 0.2
1 3.9 4.5 2.4
2 6.2 7.7 4.4
3 8.3 10.6 6.3
4 10.8 13.8 8.2
5 13.8 17.4 10.5
6 19.9 25.3 13.7
7 27.1 35.7 18.7

Figures A1: Nomogram Crosswalk figures for CAM-S LF

Figure A1a: CAM-S LF nomogram crosswalk crosswalk with MDAS and DRS-R-98

Figure A1b: CAM-S LF nomogram crosswalk with CAM-S SF and DRS-R-98

Figure A1c: CAM-S LF nomogram crosswalk with CAM-S SF and MDAS

Figure A2: Nomogram Crosswalk figures for MDAS

Figure A2a: MDAS nomogram crosswalk with CAM-S LF and DRS-R-98

Figure A2b: MDAS nomogram crosswalk with CAM-S SF and DRS-R-98

Figure A2c: MDAS nomogram crosswalk with CAM-S SF and CAM-S LF

Figure A3: Nomogram Crosswalk figures for DRS-R-98

Figure A3a: DRS-R-98 nomogram crosswalk with MDAS and CAM-S LF

Figure A3b: DRS-R-98 nomogram crosswalk with MDAS and CAM-S SF

Figure A3c: DRS-R-98 nomogram crosswalk with CAM-S LF and CAM-S SF

Figure A4: Nomogram Crosswalk figures for CAM-S SF

Figure A4a: CAM-S SF nomogram crosswalk with MDAS and DRS-R-98

Figure A4b: CAM-S SF nomogram crosswalk with MDAS and CAM-S LF

Figure A4c: CAM-S SF nomogram crosswalk with DRS-R-98 and CAM-S LF

Sensitivity/Supplemental Analyses

This section contains analyses that are more exploratory in nature, and could be supplemental to the manuscript.

Information plots using only first threshold

These analyses explore the contribution the second and third thresholds have on the overall information levels of the instruments.

Figure S1: Test Information Curve using only the first threshold

Figure S2: Difference in Information curves between dichotomous and polytomous outcomes

Figure S3: Difference in measurement error between dichotomous and polytomous outcomes

Figure S4: Boxplot of standard error of measurement for dichotomous model (from Mplus)

The delirium intensity has been cut into bins of size = 0.2. Boxplots of the SEM are shown for each bin.

Figure S5: Boxplot of standard error of measurement for polytomous model (from Mplus)

The delirium intensity has been cut into bins of size = 0.2. Boxplots of the SEM are shown for each bin.

Figure S6: Standard error of measurement for dichotomous model (from Information function)

Figure S7: Standard error of measurement for polytomous model (from Information function)